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Place lime juice, oil, Thai basil, honey and garlic in blender or food processor container; cover. Blend or process until basil is finely chopped. Reserve 1/4 of the marinade. Place shrimp in large resealable plastic bag or glass dish. Add remaining marinade; toss to coat well.
Refrigerate 15 minutes. Remove shrimp from marinade. Discard any remaining marinade. Thread 1 shrimp and 1 watermelon cube on each skewer so that the watermelon cube is in-between the 2 ends of the shrimp.
Grill over medium heat 5 minutes or just until shrimp turn pink, turning occasionally. Serve skewers drizzled with reserved marinade.